Local boundedness for solutions of a class of non-uniformly elliptic anisotropic problems

We consider a class of energy integrals, associated to nonlinear and non-uniformly elliptic equations, with integrands f(x,u,ξ) satisfying anisotropic pi,q-growth conditions of the form \sum_{i=1}^nλ_i(x)|ξ_i|^{p_i}≤f(x,u,ξ)≤μ(x)(|ξ|^q+|u|^{γ}+1) for some exponents γ≥q≥pi>1, and non-negative functions λi,μ subject to suitable summability assumptions. We prove the local boundedness of scalar local quasi-minimizers of such integrals.